Noise is a substantial problem for most DMD methods, and a common
remedy is to phrase the DMD optimization (REF ) as a total least squares problem [1]}.
Perhaps surprisingly, the solution to the orthogonal Procrustes problem (REF ) is
also the solution to the total least squares problem when the solution
is constrained to be orthogonal [2]}.
Thus, the solution (REF ) is optimal even when there is noise in both \(X\)  and \(Y\) , as long as the noise has the same distribution in \(X\)  and \(Y\) .
There are various problems closely related to the orthogonal Procrustes problem,
including the case where \(A\)  lies on the Steifel manifold (i.e., when \(A\)  is rectangular with orthonormal columns [3]}),
there is a weighting matrix [4]},
missing data [5]}, or high amounts of noise [6]}.
